Question

integration of x^3/(x^2+1)^3dx
$by usind \: substitution \: x = \tan( \alpha )$
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Answer 1

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Answer 2

Answer:

• ∫x³/(x²+1)³dx
• x= tan(α)
• dx= sec²(α)dα
• ∫(tan³α)(sec²α)/(tan²α+1)³dα
• we know 1+tan²∅=sec²∅
• ∫(tan³α)(sec²α)/(sec²α)³dα
• ∫(tan³α/sec⁴α)dα
• ∫(sin³α)(cosα)dα
• let sinα=t
• so,(cosα)dα=dt
• ∫t³dt
• t⁴/4+c
• (sin⁴α/4)+c

Step-by-step explanation: